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Applied Mathematics & Optimization

, Volume 75, Issue 2, pp 193–228 | Cite as

On a Class of Parametric (p, 2)-equations

  • Nikolaos S. Papageorgiou
  • Vicenţiu D. Rădulescu
  • Dušan D. Repovš
Article

Abstract

We consider parametric equations driven by the sum of a p-Laplacian and a Laplace operator (the so-called (p, 2)-equations). We study the existence and multiplicity of solutions when the parameter \(\lambda >0\) is near the principal eigenvalue \(\hat{\lambda }_1(p)>0\) of \((-\Delta _p,W^{1,p}_{0}(\Omega ))\). We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of \(\hat{\lambda }_1(p)>0\).

Keywords

Near resonance Local minimizer Critical group  Constant sign and nodal solutions Nonlinear maximum principle 

Mathematics Subject Classification

35J20 35J60 58E05 

Notes

Acknowledgments

V.D. Rădulescu was partially supported by the Romanian Research Council through the Grant CNCS-UEFISCDI-PCCA-23/2014. D.D. Repovš acknowledges the partial support of the Slovenian Research Agency through Grants P1-0292-0101, J1-7025-0101 and J1-6721-0101.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Nikolaos S. Papageorgiou
    • 1
  • Vicenţiu D. Rădulescu
    • 2
    • 3
  • Dušan D. Repovš
    • 4
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Department of Mathematics, Faculty of SciencesKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsUniversity of CraiovaCraiovaRomania
  4. 4.Faculty of Education and Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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